The Evolving Role of Technology in Mathematics

Technology has fundamentally changed the practice of mathematical modeling by shifting the cognitive load. Initially, the primary challenge in modeling was solving the model (i.e., performing complex calculations, solving differential equations, or manipulating algebraic expressions).

The introduction of technological tools addressed this challenge:

• Computer Algebra Systems (CAS): Tools like Mathematica, Wolfram Alpha, and MATLAB have automated symbolic manipulation and numerical computation. This allowed modelers to work with more complex, realistic problems without getting bogged down in tedious calculations.

• Dynamic and Simulation Software: Visualization tools and simulation environments (such as NetLogo or advanced spreadsheets) enable modelers to run simulations, visualize results, and test "what-if" scenarios.

This shift enabled modelers and students in an educational context to focus less on calculation and more on the higher-order skills of the modeling process: model construction (making assumptions and defining variables) and model evaluation (interpreting results and validating the model against real-world data).

AI in Mathematical Modeling Education

AI is transforming how mathematical modeling is taught. It creates new possibilities for students to engage with the modeling process.

• AI as a Tutor: Intelligent Tutoring Systems (ITS) can provide personalized, step-by-step feedback as students build a model. It can spot common errors in their logic or calculations and offer hints.

• AI as a Tool: Generative AI (such as ChatGPT) can serve as a powerful assistant. A student can ask it to:

  • "Explain the assumptions behind this epidemiological model."

  • "Write the Python code to simulate this model."

  • "Help me brainstorm variables that affect the price of coffee."

• AI as a Collaborator: In more advanced settings, AI can serve as a valuable partner for mathematical modeling. A student can build a simple model, and an AI can run complex simulations or find patterns in a dataset that the student can then use to refine their model. This fosters student agency, allowing them to tackle more complex and authentic problems.